CEPAL Review no. 124

148 CEPAL Review N° 124 • April 2018
expectations, since economic agents correct their expectations on the basis of past forecasting errors.
In other words, expected inflation, p t e , would be modelled as a weighted-average of past inflation rates,
with heavier weights attaching to more recent data. The Phillips curve would thus assume the form:
p t
= j p t
e
+ g (u t
– u n
)+ e t
(2)
where p t
is current inflation, and p t
e
is expected inflation in period t, formulated as a weighted-average
of past inflation rates, u t
is the current unemployment rate and u n
the natural rate.
This gave agents’ expectations a fundamental role in the construction and execution of economic
policies. Nonetheless, it was subsequently realized that adaptive expectations would lead economic
agents to commit systematic forecasting errors, which is not realistically sustainable.
This finding triggered a revolution in macroeconomic theory between the 1970s and 1980s, driven
by the forward-looking rational expectations hypothesis, attributed to Lucas (1972) and Sargent (1971).
According to these authors, economic agents predict future inflation by considering all of the information
available to them up to the current period, and not just a combination of past data. Thus, expectations
become a function of the set of all data available up to t, so the Phillips curve also needs a forwardlooking
component.
2. New-Keynesian Phillips Curve
A new approach to the Phillips curve has been widely discussed in recent decades. Taylor (1980)
and Calvo (1983) laid the foundations for the modern analysis of inflation by examining price and
wage choices from the perspective of forward-looking families and businesses. In this version, the
curve is deduced as a relation between inflation and firms’ marginal cost. This formulation, called the
New-Keynesian Phillips Curve, is based on two structural equations, namely:
p t
= qp t-1
+ (1 – q)p t
* (3)
and
(4)
In equation (3), p t
is the aggregate price level and p t
* denotes the price level derived from
enterprise profit maximization, both in logarithmic form; and q (0 < q < 1) is the fraction of firms that do
not adjust their prices optimally in t. Equation (3) thus introduces a degree of price rigidity, since only
a fraction (1 – q) of the firms can optimally adjust their prices in t, while the others retain the prices of
the previous period.
Equation (4) can be derived formally by maximizing the present value of firms’ expected profits,
specifying the optimal price chosen by firms as a function of q, the real marginal cost, and a
discount factor b (Calvo, 1983). In other words, in the absence of friction or adjustment costs, firms
would set their prices equal to marginal cost in each period. In practice, however, firms do not change
their prices in every period; so the definition of
is not appropriate in this context. Prices
have to be formed on the basis of the expected behaviour of marginal cost, so as to maximize the
present value of expected profit. Thus, by defining inflation in period t as p t
= p t
– p t-1
and combining
equations (3) and (4), NKPC can be written as:
p t
= lcm t
+ g f
E t
{p t+1
} (5)
Business cycles, expectations and inflation in Brazil: a New-Keynesian Phillips curve analysis